A Fast and Robust Optimization Methodology for a Marine Ecosystem Model Using Surrogates

Model calibration in climate science plays a key role for simulations and predictions of the earth's climate system. Straightforward attempts by employing the high-fidelity (or fine) model under consideration directly in an optimization loop using conventional optimization algorithms are often tedious or even infeasible, since typically a large number of computationally expensive fine model evaluations are required. The development of faster methods becomes critical, where the optimization of coupled marine ecosystem models, which simulate biogeochemical processes in the ocean, are a representative example. In this paper, we introduce a surrogate-based optimization (SBO) methodology where the expensive fine model is replaced by its fast and yet reasonably accurate surrogate. As a case study, we consider a representative of the class of one-dimensional marine ecosystem models. The surrogate is obtained from a temporarily coarser discretized physics-based low-fidelity (or coarse) model. and a multiplicative response correction technique. In our previous work, a basic formulation of this surrogate was sufficient to create a reliable approximation, yielding a remarkably accurate solution at low computational costs. This was verified by model generated, attainable data. The application on real data is covered in this paper. Enhancements of the basic formulation by utilizing additionally fine and coarse model sensitivity information as well as trust-region convergence safeguards allow us to further improve the robustness of the algorithm and the accuracy of the solution. The trade-offs between the solution accuracy and the extra computational overhead related to sensitivity calculation will be addressed. We demonstrate that SBO is able to yield a very accurate solution at still low computational costs. The optimization process - when compared to the direct fine model optimization - is significantly speed up to about 85 \%.

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